Various objective techniques (retinoscopy, autorefraction, photorefraction) can be used to measure the spherical and cylindrical refractive errors of the human eye. They are fast and constitute an attractive alternative to performing a subjective refraction. Objective refraction is not only useful but often essential, for example, when examining young children and patients with mental or language difficulties. However, one major concern is the ability to properly determine objectively the refraction of the observer. Since all those objective methods are based on the light reflected from the retina and emerging from the eye, the ocular aberrations reduce the accuracy of the measurement. The eye suffers from many higher-order aberrations beyond defocus and astigmatism, which introduce defects on the pattern of light detected. Thus, photorefractive methods are based on paraxial optical analysis, and it has been shown that there can be a significant degree of measurement uncertainty when the spherical aberration of the normal human eye is considered. Aberrations also influence the retinoscopic measure. Although autorefractors provide reliable measurements of the refractive state of the eye, their limitations in accuracy and repeatability are well known. For example, there are discrepancies between autorefractive and subjective measurements, especially with astigmatism, or when the degree of ametropia is large. Such discrepancies are described in M. Elliott et al, xe2x80x9cRepeatability and accuracy of automated refraction: A comparison of the Nikon NRK-8000, the Nidek AR-1000, and subjective refraction,xe2x80x9d Optom. Vis. Sci. 74,434-438, 1997; J. J. Walline et al, xe2x80x9cRepeatability and validity of astigmatism measurements,xe2x80x9d J. Refract. Surgery 15, 23-31, 1999; and A. M. Thompson et al xe2x80x9cAccuracy and precision of the Tomey ViVA infrared photorefractor,xe2x80x9d Optom. Vis. Sci. 73, 644-652, 1996. Also, retinoscopy and autorefraction usually disagree to some extent, as described in E. M. Harvey et al, xe2x80x9cMeasurement of refractive error in Native American preschoolers: Validity and reproducibility of autorefraction,xe2x80x9d Optom. Vis Sci. 77, 140-149, 2000.
Patients"" preference with regard to autorefraction is described in M. A. Bullimore et al, xe2x80x9cPatient Acceptance of Auto-Refractor and Clinician Prescriptions: A Randomized Clinical Trial,xe2x80x9d Visual Science and its Applications, 1996 Technical Digest Series, Vol. 1, Optical Society of America, Washington, D.C., pp. 194-197, and in M. A. Bullimore et al, xe2x80x9cThe Repeatability of Automated and Clinician Refraction,xe2x80x9d Optometry and Vision Science, Vol 75, No. 8, August, 1998, pp. 617-622. Those articles show that patients prefer the clinician""s refraction; for example, the former article states that the autorefractor has a rejection rate around 11% higher than the clinician. The difference in rejection rates suggests that autorefraction is less accurate than the clinician""s prescription. Thus, the state of the art in autorefraction provides room for improvement.
In that context, the development of an objective method that makes use of the higher-order aberrations of the eye and provides accurate estimates of the subjective refraction is an important challenge. Such a method would be extremely useful, for example, to refine refractive surgery. As more patients inquire about refractive surgical procedures, the accurate measurement of refractive errors prior to surgery becomes more important in assessing refractive outcome. Another important issue regards the aging of the eye. A difference has been found between subjective refraction and autorefraction for different age groups. That difference probably comes from the fact that the ocular aberrations increase with age. The age dependency is described in L. Joubert et al, xe2x80x9cExcess of autorefraction over subjective refraction: Dependence on age,xe2x80x9d Optom. Vis. Sci. 74,439-444, 1997, and in A. Guirao et al, xe2x80x9cAverage optical performance of the human eye as a function of age in a normal population,xe2x80x9d Ophth. Vis. Sci. 40, 203-213, 1999. An objective method that considers the particular aberration pattern of the subject would provide reliable estimates for all the age groups. Such a method could also automatically give a value of refraction customized for every pupil size and light level, since both aberrations increase with pupil size and visual acuity depends on luminance conditions.
The higher-order aberrations of the eye can be now measured quickly, accurately and repetitively, for instance, with a Shack-Hartmann sensor. A method and apparatus for doing so are taught in U.S. Pat. No. 5,777,719 to Williams et al. It seems then almost mandatory to optimize the use of this new information in a more accurate instrument.
The simplest case of vision correction is shown in FIG. 1A, in which the only error is of focus. That is, the rays R passing through the edge of the pupil 103 of the eye 102 are focused on a paraxial plane 110 which is spatially separated from the plane 112 of the retina. Accordingly, the only correction required is to shift the plane of focus from the paraxial plane 110 to the retinal plane 112. The images before, at and after the paraxial plane 110 are shown as 124, 126 and 128, respectively.
The diagram in FIG. 1B shows an example of the image formation by a myopic eye 102xe2x80x2 with negative spherical aberration. Without spherical aberration, all the rays Rxe2x80x2 would focus on the paraxial plane 110, and then the refraction of the eye would be calculated from the spherical negative lens required to displace the focus plane to the plane 112 lying on the retina. However, due to spherical aberration, the rays R passing through the edge of the pupil 103 converge at a plane 104 closer to the eye (marginal plane). That simple example shows how the distribution of rays in different planes produces images 114-122 with different quality. The refraction of that eye should be the one required for displacing a plane of xe2x80x9cbest imagexe2x80x9d to the retina.
A similar phenomenon occurs when astigmatism must be corrected. Depending on the higher-order aberrations of the eye, to maximize the image quality, the amount of astigmatism to correct could be different, beyond the paraxial zone, from that corresponding to the Sturm""s interval (distance between the two focal planes determined by astigmatism).
Such a situation is shown in FIG. 1C. The rays Rxe2x80x3 and Rxe2x80x2xe2x80x3 from different locations in the pupil 103 of the eye 102xe2x80x3 have focal points which are not coincident or even coaxial. Thus, the images taken at various locations are shown as 130, 132 and 134. In cases in which not all aberrations can be corrected, or in which all aberrations can be only partially corrected, it is necessary to determine which of the images 130, 132 and 134 is the best image.
The best image is not, or at least not necessarily, achieved by correcting the defocus and astigmatism corresponding to the paraxial approximation, which does not consider the effect of higher order aberrations. The question then is what is such a xe2x80x9cbest image.xe2x80x9d By a geometrical ray tracing the answer is that the best image would correspond to a plane where the size of the spot is minimum. That plane, shown in FIG. 1B as 106, is called the plane of least confusion (LC) and, for example, for a system aberrated with spherical aberration lies at xc2xe of the distance between the paraxial and marginal planes. Another candidate is the plane 108 where the root-mean-square (RMS) radius of the spot is minimum. In the example of FIG. 1B, that plane lies midway between the marginal and paraxial planes. However, the spots determined geometrically do not accurately reflect the point spread function (PSF), which is the computed retinal image based on the results of the wavefront sensor and which should be calculated based on the diffraction of the light at the exit pupil. The distribution of light in a real image is usually very different from the image predicted geometrically with ray tracing. Any consideration about image quality should be done using diffraction theory.
The higher-order aberrations are combined with lower-order aberrations, which is known as xe2x80x9cbalancing.xe2x80x9d One of the main properties of the popular Zernike polynomials is that they represent balanced aberrations. Second-order polynomials, Z20,xc2x12, represent defocus and astigmatism. For instance, spherical aberration is balanced with defocus in the term Z04; the terms Z4xc2x12 are balanced with astigmatism, etc. The aberration balancing is an attractive concept in the sense that a minimum RMS of the aberrated wavefront suggests the achievement of the best image. Hence, the RMS of the wave aberration has been used as a measure of how aberrated an eye is and as a metric of image quality: the lower the RMS, the better the image quality. A fact that has supported that use is that the RMS correlates, for small aberrations, with another popular metric also used as a criterion of image quality, the Strehl ratio, defined as the peak of irradiance of the PSF. A large value of Strehl ratio indicates a good image quality. For small aberrations, Strehl ratio and RMS of the wave aberration are inversely proportional: when the Strehl ratio is maximum, the RMS is minimum. Several equations have been derived to express that relationship; one of the best known is:                               S          =                      exp            ⁡                          (                              -                                                      (                                                                                            2                          ⁢                          π                                                λ                                            ⁢                                              xe2x80x83                                            ⁢                      RMS                                        )                                    2                                            )                                      ,                            (        1        )            
where S is the Strehl ratio and xcex is the wavelength.
The wave aberration is usually decomposed into Zernike basis functions after being measured, W=xcexa3anmZnm. An advantage of that is that the RMS of the wave aberration can then be obtained easily from the Zernike coefficients: RMS2=xcexa3(anm)2. Thus, any correction of the refractive errors of the eye, or of a set of higher-order aberrations, could be determined by setting to zero the corresponding Zernike coefficients (a20,xc2x12=0 to correct refractive errors, or for example a3xc2x11=0 to correct coma). But, again, the image analysis based on diffraction shows the failure in general of that idea. When aberrations are large, a maximum Strehl ratio can be obtained with nonoptimally balanced aberrations (i.e., not a minimum in the RMS). More concretely, when the RMS of the wave aberration is larger than about 0.15 wavelengths, Eq. (1) is not longer valid. In comparison, the value for example of the spherical aberration of the normal average eye is 3-4 wavelengths for a pupil diameter of 6 mm. Therefore, the sphere and cylinder required to prescribe refraction and achieve the best image quality can not be obtained from the assumption of minimum RMS. The same occurs if one pretends to correct spherical aberration or coma, for instance. The balanced secondary spherical aberration (polynomial Z60) and the balanced secondary coma (Z5xc2x11) do not give the maximum Strehl ratio for large aberrations.
The RMS minimization technique uses the coefficients a02 and a2xc2x12 from the Zernike expansion and results in the correction of defocus and astigmatism. The paraxial technique extracts the total defocus and astigmatism in the wave aberration.
Both of the above techniques, which are based on the pupil plane and use the data of the wave aberration itself, fail when higher-order aberrations increase. In particular, the difference between the subjective and objective determinations of the aberration increases with the RMS of the wavefront aberration, as shown in FIG. 1D, in which curve (1) indicates the RMS minimization technique and curve (2) indicates the paraxial technique. The higher-order aberration in the population has been found to average 0.3xcexc, as shown in FIG. 1E. As a consequence, the above-noted techniques do not work for approximately half of the population and can introduce errors of up to one diopter.
From the above, it will be apparent that a need exists in the art to overcome the above-noted deficiencies of the prior art. It is therefore a primary object of the invention to provide an objective measurement of higher-order aberrations of the eye which provides an accurate estimate for the subjective refraction.
It is another object of the present invention to provide a reliable measurement for multiple pupil sizes, light levels, and ages.
It is yet another object of the invention to determine the metric which best expresses the optimal image for vision.
It is still another object of the invention to provide reliable measurement for a greater percentage of the population.
The above and other objects are achieved through a computational system and method which determine the refractive error of the eye from measurements of its wave aberration. The procedure calculates the combination of sphere and cylinder that optimizes one or more metrics based on the distribution of light in the retinal image, which is affected by the higher-order aberrations. The retinal image, which is the distribution of light on the retinal or image plane, is calculated from the results of a Shack-Hartmann or other detector. A metric based directly on the retinal image can be computed, or a metric which is a proxy for the retinal image can be used. Any metric on the image plane can be used, and one or more metrics can be used. The method yields an optimum image that is correlated with the subjective best retinal image. Since the method is computational, a computer is the only hardware required, and it can be combined with a wavefront sensor in a compact instrument.
The present invention takes into account the fact that while pupil-plane metrics do not accurately predict the subjective refraction, image-plane metrics do. While the techniques of the prior art were adequate for only about 25% of subjects with a precision of xc2x10.25 D or 50% of subjects with a precision of xc2x10.5 D, the present invention will provide suitable correction for most subjects Keith errors  less than 0.25 D.
For estimation of the subjective refraction, both the peak and the tails of the metric value can be used; that is, information from the curve of the metric other than the location of the maximum can be used. For example, the width of the curve can be used for xe2x80x9ctolerancing,xe2x80x9d since a narrower curve indicates a lower tolerance and thus a more critical need for accurate correction. An example is better fitting of a contact lens which corrects sphere and not astigmatism for subjects with a large tolerance to astigmatism.
Unlike autorefraction, which is limited to a single pupil size, the present invention is not so limited. The present invention allows the subjective refraction to be calculated for any pupil size equal to or smaller than the pupil size over which the wave aberration was measured.
The present invention is further directed to a second application flowing from the above-noted computational system and method. While spectacles and contact lenses have been successfully used to correct defocus and astigmatism (second-order aberrations), they leave the higher-order aberrations uncorrected. For small pupils, a conventional correction offers a sufficient improvement. However, it has been found that the higher-order aberrations have a significant impact on the retinal image quality in normal eyes for large pupils and also for small pupils in old subjects or in abnormal subjects such as post refractive surgery or keratoconus patients. Indeed, the use of an adaptive optical system has successfully corrected higher-order aberrations and provided normal eyes with supernormal optical quality. Recent developments make viable the idea of implementing supercorrecting procedures. Thus, lathe technology allows the manufacture of contact lenses with nearly any aberration profile, and there is an ongoing effort to refine laser refractive surgery to the point that it can correct other defects besides conventional refractive errors.
While achieving the correction of all of the aberrations is desirable, that implies a customized correction with many degrees of freedom. Moreover, the higher the order of the aberration, the lower the tolerance to mismatch and the greater the accuracy of the correction required to be effective. A tradeoff that accomplishes the reduction of aberrations while implying a relatively simple robust correction implements a customized correction of only a certain set of higher-order aberrations such as, for example, coma and spherical aberration. Coma and spherical aberration are particularly important because those aberrations are the ones with larger values in the human eye and have a large tolerance to decentration. However, the present invention is general and may similarly be implemented to any other set of aberrations.
In short, if it is possible to detect more aberrations than can be corrected, the aberrations to be corrected are selected, or all of the aberrations are corrected partially. For example, if n aberrations can be measured, mxe2x89xa6n aberrations can be corrected. The present invention permits a determination of the values of the compensation aberrations in the correcting method required to optimize the subject""s vision. For example, in some countries it is common to correct for sphere but not astigmatism. The present invention provides an improved way to do so. As another example, since the eye is not stable, residual aberrations cannot be avoided. The present invention minimizes problems caused by such residual aberrations.
Thus, the second part of the present invention provides a computational procedure to design an optimum pattern of a customized correction of a few aberrations of the eye besides astigmatism and defocus. The procedure considers the effect of the remaining aberrations that have been left uncorrected to calculate the adequate values of the aberrations to be corrected in order to achieve the best image quality.
Several metrics can be used to describe retinal image quality. The computational procedure calculates the prescription of the refractive error of a subject based on the optimum values of those metrics.
The present invention is based on the surprising discovery that when correction is carried out in accordance with a metric measured on the image plane, it is not necessary to take into account the brain""s preference in image quality. The use of a metric which takes the brain into account produces no significant difference. By contrast, it was originally believed that corrections would have to take into account the brain""s preference in image quality. For that reason, techniques from astronomy, in which such effects do not arise, would not have been considered. Thus, computation is significantly simplified over what the inventors originally thought was required.
Higher-order aberrations influence the optimal subjective refraction and the tolerance to miscorrections. Pupil-plane metrics (e.g., wave aberration RMS) do not accurately predict the subjective refraction. Thus, wavefront sensors can improve objective refraction by using image-plane metrics (or quantities which function as proxies for image-plane metrics) to incorporate the effect of higher-order aberrations.
The present invention allows the prediction of subjective refraction from any reliable wavefront device and performs substantially better than current autorefractors. Some limitations of autorefractors are: the pupil size; the level of radiation (often low) returning from the retina and analyzed by the detector; the fact that the target, such as a grating, is blurred twice in its double pass through the eye""s optics; and the fact that current autorefractors estimate three and only three parameters (sphere, cylinder and axis). By contrast, the present invention can optimize the correction for any number of aberrations, from defocus alone to as many aberrations as have been measured. The present invention is applicable to any technique for correction, including contact lenses, intraocular lenses, spectacles, laser refractive surgery, and adaptive optics. Further, the present invention allows prescribing a correction based on the patient""s tolerance to departures from the optimum correction. For example, the patient""s tolerance to a contact lens that corrects only sphere and not astigmatism can be objectively estimated.
With regard to the above-mentioned proxy metric, it has been found empirically that in many subjects, the best image can be predicted from the aberration coefficients. If the aberration coefficients can be used to calculate two results whose errors have opposite signs, the proxy metric can be a simple average or a weighted average.